Another really neat theorem!

**Chris11** · June 24th 2010, 08:53 PM

This is not for help or anything; just a neat factoid. The number of odd numbers in the nth row of pascal's triangle is $2^k$ , where k is the the number of ones occuring in the binary representation of n.

**simplependulum** · June 25th 2010, 12:36 AM

The generalization of this theorem is that if $n = a_m a_{m-1}... a_0$ the representation of $n$ in base prime $p$ , then the number of the binomial coefficients which are prime to $p$ is $(a_0 + 1 )(a_1 + 1 )...(a_m + 1 )$ .

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Another really neat theorem!

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